Dear MHF members,

my problem reads as follows. I have some ideas about some parts of the problem but I would like to share it completely because I find the problem nice.

Problem. Consider the system , where is a constant matrix with only two distinct eigenvalues and Suppose that the Jordan form of has Jordan blocks corresponding to and blocks corresponding to , where is a Jordan block.

- How many linearly independent eigenvectors does have?
- Suppose that is not an eigenvector but satisfies . How many linearly independent solution vectors are there?
- Suppose that the Jordan blocks occur down the diagonal of the in the order stated above. Which matrix elements of are non-zero and what are their values?

Thanks a lot.

bkarpuz